One thing that I'd add to Andrew's comment is that steel often fails slowly. So if you watch the repaired area for cracks, chipping paint, etc, then it might be possible to predict a failure.
It might depend a bit on one's riding. Distances, alternative transportation, how you'll get home, etc. RACING? Group Rides?
At times an imminent failure is an incidental finding. At other times a full failure happens at the most inopportune moment.
Looking at the previous repair I have troubles discerning exactly how it was done. Was some kind of body filler used? That could make it more difficult to visualize the repair, as well as monitor for damage progression.
You can think of that dropout as essentially channel iron with 2 flanges and webbing between. Much of the strength of the channel is at the flanges.
From the second photo it looks like the person doing the repair ground into the flanges somewhat, but didn't fully fill his grind. That may indicate that there was a "V" cut under all the welds or brazing areas.
The actual weld may be strong enough, although I would have expected continuing welding across all parts of the flanges where one would have a significant amount of strength, as well as resistance to flex.
So, you have 3 options.
1) ride as-is. Perhaps strip the repair to inspect more carefully.
2) Verify metal used. Strengthen repair by adding a gusset in the slot, and making sure the flanges are properly filled/strengthened.
3) Replace one or both rear dropouts. Likely the most expensive option, but one ends up with "good as new".
£230 sounds high, but perhaps the seller would negotiate.